Michael Grinfeld, Iulian Stoleriu
Abstract:
We employ the Pade approximation to derive a set of new partial
differential equations, which can be put forward as possible models
for phase transitions in solids. We start from a nonlocal free energy
functional, we expand in Taylor series the interface part of this energy,
and then consider gradient flows for truncations of the resulting expression.
We shall discuss here issues related to the existence and uniqueness
of solutions of the newly obtained equations, as well as the convergence
of the solutions of these equations to the solution of a nonlocal version
of the Allen-Cahn equation.
Submitted November 1, 2006. Published December 5, 2006.
Math Subject Classifications: 47H20, 45J05, 35K55, 41A21.
Key Words: Gradient flow; van der Waals energy;
integro-differential equation; Pade approximants.
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| Michael Grinfeld Department of Mathematics, University of Strathclyde 26 Richmond Street, G1 1XH Glasgow Scotland, United Kingdom email: m.grinfeld@strath.ac.uk | |
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Iulian Stoleriu Faculty of Mathematics, "Al. I. Cuza" University Bvd. Carol I, No. 11, 700506 Iasi, Romania. EML Research gGmbH, Schloss Wolfsbrunnenweg 33 69118 Heidelberg, Germany email: iulian.stoleriu@uaic.ro, iulian.stoleriu@eml-r.villa-bosch.de |
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